Matrix Matchup Worksheet
Algebra II • Precalculus Unit: Matrices
Matrix Matchup Worksheet
Determine dimensions, check multiplication compatibility, and state resulting product size. Do not solve.
Name:
Date: Per:
RULE Size = \(r \times c\) (Rows \(\times\) Columns)
Multiplication Defined If: \(m \times \mathbf{k}\) and \(\mathbf{k} \times n\)
Resulting Size: \(m \times n\)
#1
\(\begin{bmatrix} 2 & -1 \\ 4 & 3 \end{bmatrix} \cdot \begin{bmatrix} 5 & 0 \\ -2 & 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#2
\(\begin{bmatrix} 1 & 3 & -2 \\ 0 & 4 & 5 \end{bmatrix} \cdot \begin{bmatrix} 2 & 1 \\ -1 & 3 \\ 4 & 0 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#3
\(\begin{bmatrix} 4 & 1 \\ -2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 1 & 2 \\ 0 & -1 \\ 3 & 4 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#4
\(\begin{bmatrix} 3 & -2 & 5 \end{bmatrix} \cdot \begin{bmatrix} 4 \\ 1 \\ -2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#5
\(\begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix} \cdot \begin{bmatrix} 5 & 0 & -4 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#6
\(\begin{bmatrix} 1 & 4 \\ 2 & -3 \\ 0 & 5 \end{bmatrix} \cdot \begin{bmatrix} 3 & -1 \\ 2 & 4 \\ 1 & 0 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#7
\(\begin{bmatrix} 2 & -1 & 3 \\ 0 & 4 & -2 \end{bmatrix} \cdot \begin{bmatrix} 5 \\ 1 \\ -3 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#8
\(\begin{bmatrix} 4 & -2 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 & 3 \\ -2 & 5 & 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#9
\(\begin{bmatrix} 3 \\ -1 \end{bmatrix} \cdot \begin{bmatrix} 2 \\ 4 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#10
\(\begin{bmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \\ 2 & 0 & -2 \end{bmatrix} \cdot \begin{bmatrix} 4 & -1 \\ 2 & 3 \\ 0 & 5 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
Matrix Matchup Worksheet • Page 2
Part II: Mixed & Vector Dimensions (Problems 11–20)
Name:
#11
\(\begin{bmatrix} 1 & 2 \\ 3 & 0 \\ -1 & 4 \\ 2 & 1 \end{bmatrix} \cdot \begin{bmatrix} 2 & -1 & 3 \\ 0 & 4 & 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#12
\(\begin{bmatrix} 3 & -1 \\ 2 & 4 \\ 0 & 5 \end{bmatrix} \cdot \begin{bmatrix} 1 & -2 \\ 4 & 3 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#13
\(\begin{bmatrix} 2 & 1 & 0 & -3 \\ 4 & -1 & 5 & 2 \end{bmatrix} \cdot \begin{bmatrix} 1 & -2 & 3 & 0 \\ 0 & 4 & -1 & 2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#14
\(\begin{bmatrix} 1 & -3 & 2 & 4 \end{bmatrix} \cdot \begin{bmatrix} 2 \\ 0 \\ -1 \\ 5 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#15
\(\begin{bmatrix} 5 & -2 \\ 1 & 3 \end{bmatrix} \cdot \begin{bmatrix} 0 & 4 & -1 & 2 \\ 3 & 1 & 2 & -3 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#16
\(\begin{bmatrix} 2 \\ -1 \\ 4 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 & 3 \\ -2 & 4 & 5 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#17
\(\begin{bmatrix} 3 \\ -2 \\ 1 \\ 4 \end{bmatrix} \cdot \begin{bmatrix} 2 & -5 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#18
\(\begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 1 \\ 0 & 4 & -2 \end{bmatrix} \cdot \begin{bmatrix} 2 & 0 & 1 \\ -1 & 1 & 3 \\ 4 & -2 & 0 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#19
\(\begin{bmatrix} 2 & 4 & -1 \\ 3 & 0 & 5 \end{bmatrix} \cdot \begin{bmatrix} 1 & -2 & 3 \\ 0 & 4 & -1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#20
\(\begin{bmatrix} 3 \end{bmatrix} \cdot \begin{bmatrix} 2 & -1 & 4 & 0 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
Matrix Matchup Worksheet • Page 3
Part III: Non-Square & Rectangular Pairs (Problems 21–30)
Name:
#21
\(\begin{bmatrix} 1 & 0 & -2 & 3 \\ 2 & 1 & 4 & -1 \\ 0 & 3 & -1 & 2 \end{bmatrix} \cdot \begin{bmatrix} 2 & 1 \\ -1 & 0 \\ 3 & 2 \\ 0 & 4 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#22
\(\begin{bmatrix} 2 & -1 & 3 \\ 1 & 0 & 4 \\ -2 & 3 & 1 \\ 0 & 2 & -1 \end{bmatrix} \cdot \begin{bmatrix} 3 \\ -2 \\ 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#23
\(\begin{bmatrix} 3 & -1 & 2 \\ 0 & 4 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & 2 & 0 \\ -1 & 3 & 4 \\ 2 & 0 & 1 \\ 4 & -2 & 3 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#24
\(\begin{bmatrix} 2 & -1 & 3 \end{bmatrix} \cdot \begin{bmatrix} 1 & 4 & 0 \\ -2 & 3 & 1 \\ 0 & -1 & 2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#25
\(\begin{bmatrix} 1 & -2 \\ 3 & 0 \\ 4 & -1 \end{bmatrix} \cdot \begin{bmatrix} 2 & 1 & 0 \\ -1 & 3 & 4 \\ 0 & 2 & -3 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#26
\(\begin{bmatrix} 5 \\ -2 \end{bmatrix} \cdot \begin{bmatrix} -4 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#27
\(\begin{bmatrix} 3 & -1 \\ 2 & 0 \\ 1 & 4 \\ -3 & 2 \end{bmatrix} \cdot \begin{bmatrix} 4 \\ -1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#28
\(\begin{bmatrix} 1 & -1 & 2 & 0 \\ 3 & 4 & -2 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 & 0 & 2 \\ 0 & 2 & -1 & 1 \\ 3 & 1 & 0 & -2 \\ -1 & 0 & 4 & 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#29
\(\begin{bmatrix} 2 & -1 \\ 4 & 3 \\ 0 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & -2 & 0 & 3 \\ 4 & 1 & -1 & 2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#30
\(\begin{bmatrix} 1 \\ -2 \\ 4 \\ 0 \end{bmatrix} \cdot \begin{bmatrix} 3 \\ 1 \\ -1 \\ 2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
Matrix Matchup Worksheet • Page 4
Part IV: Complex Dimensions & Boundary Cases (Problems 31–40)
Name:
#31
\(\begin{bmatrix} 1 & 0 & 2 & -1 \\ -2 & 1 & 0 & 3 \\ 0 & 4 & 1 & -2 \\ 2 & -1 & 3 & 0 \end{bmatrix} \cdot \begin{bmatrix} 3 & -1 \\ 2 & 4 \\ 0 & 1 \\ -2 & 0 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#32
\(\begin{bmatrix} 2 & -5 \end{bmatrix} \cdot \begin{bmatrix} 4 & 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#33
\(\begin{bmatrix} 1 & -2 & 3 \\ 0 & 4 & 1 \end{bmatrix} \cdot \begin{bmatrix} 2 & 0 & 1 & -3 \\ -1 & 3 & 4 & 0 \\ 0 & 2 & -1 & 1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#34
\(\begin{bmatrix} 2 & 1 & -1 & 0 \\ 0 & 3 & 4 & 2 \\ -1 & 0 & 2 & 1 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 & 2 & -1 \\ 3 & 1 & 0 & 4 \\ 2 & -1 & 3 & 0 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#35
\(\begin{bmatrix} 1 & -1 & 2 \\ 0 & 3 & 1 \\ 4 & 0 & -2 \\ 2 & 1 & 0 \end{bmatrix} \cdot \begin{bmatrix} 2 & 1 & 0 \\ -1 & 3 & 4 \\ 0 & 2 & -1 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#36
\(\begin{bmatrix} 3 & -1 & 0 & 2 \end{bmatrix} \cdot \begin{bmatrix} 1 & 4 \\ 2 & -1 \\ -3 & 0 \\ 0 & 2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#37
\(\begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix} \cdot \begin{bmatrix} 2 & 1 \\ 0 & -3 \\ 4 & 2 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#38
\(\begin{bmatrix} 2 & 0 & -1 \\ 3 & 4 & 2 \\ -1 & 1 & 0 \end{bmatrix} \cdot \begin{bmatrix} 5 \\ -2 \\ 3 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#39
\(\begin{bmatrix} 1 & -2 \\ 3 & 0 \\ 0 & 4 \\ -1 & 1 \end{bmatrix} \cdot \begin{bmatrix} 2 & 1 & 0 & -3 \\ -1 & 3 & 2 & 1 \\ 4 & 0 & -2 & 5 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
#40
\(\begin{bmatrix} 2 & -1 & 3 & 0 \\ 1 & 4 & -2 & 5 \end{bmatrix} \cdot \begin{bmatrix} 3 \\ -2 \\ 1 \\ 4 \end{bmatrix}\)
1st: × 2nd: ×
Defined? Yes No
Result: ×
Concept Check Dimension Synthesis
A. If \(A\) is \(3 \times 5\) and \(AB\) has size \(3 \times 2\), find size of \(B\):
×
B. Can you compute \(M \cdot M\) if \(M\) is not square?
Yes No
